The interaction between synoptic eddy and low-frequency flow (SELF) has been recognized for decades to play an important role in the dynamics of the low-frequency variability of the atmospheric circulation. In this three-part study a linear framework with a stochastic basic flow capturing both the climatological mean flow and climatological measures of the synoptic eddy flow is proposed. Based on this linear framework, a set of linear dynamic equations is derived for the ensemble-mean eddy forcing that is generated by anomalous time-mean flows. By assuming that such dynamically determined eddy-forcing anomalies approximately represent the time-mean anomalies of the synoptic eddy forcing and by using a quasi-equilibrium approximation, an analytical nonlocal dynamical closure is obtained for the two-way SELF feedback. This linear closure, directly relating time-mean anomalies of the synoptic eddy forcing to the anomalous time–mean flow, becomes an internal part of a new linear dynamic system for anomalous time–mean flow that is referred to as the low-frequency variability of the atmospheric circulation in this paper. In Part I, the basic approach for the SELF closure is illustrated using a barotropic model. The SELF closure is tested through the comparison of the observed eddy-forcing patterns associated with the leading low-frequency modes with those derived using the SELF feedback closure. Examples are also given to illustrate an important role played by the SELF feedback in regulating the atmospheric responses to remote forcing. Further applications of the closure for understanding the dynamics of low-frequency modes as well as the extension of the closure to a multilevel primitive equation model will be given in Parts II and III, respectively.

[1] The relationship between the static stability N 2 and the mixing in the tropopause inversion layer (TIL) is investigated using in situ aircraft observations during SPURT (trace gas transport in the tropopause region). With a new simple measure of mixing degree based on O 3 -CO tracer correlations, high N 2 related to an enhanced mixing in the extratropical mixing layer is found. This relation becomes even more pronounced if fresh mixing events are excluded, indicating that mixing within the TIL occurs on a larger than synoptic timescale. A temporal variance analysis of N 2 suggests that processes responsible for the composition of the TIL take place on seasonal timescales. Using radiative transfer calculations, we simulate the influence of a change in O 3 and H 2 O vertical gradients on the temperature gradient and thus on the static stability above the tropopause, which are contrasted in an idealized nonmixed atmosphere and in a reference mixed atmosphere. The results show that N 2 increases with enhanced mixing degree near the tropopause. At the same time, the temperature above the tropopause decreases together with the development of an inversion and the TIL. In the idealized case of nonmixed profiles the TIL vanishes. Furthermore, the results suggest that H 2 O plays a major role in maintaining the temperature inversion and the TIL structure compared to O 3 . The results substantiate the link between the extratropical mixing layer and the TIL.

[1] NCEP-NCAR reanalysis data from 1948 to 2001 are used to examine the relationship between the North Atlantic Oscillation (NAO) and the North Atlantic sea surface temperature anomaly (SSTA) tripole. It is demonstrated that the atmospheric anomalies associated with NAO produce tripole-like sea surface temperature (SST) anomalies; in turn, the SSTA tripole produces NAO-like atmospheric anomalies. Therefore, a positive feedback between the NAO and the SSTA tripole is suggested. The results are statistically significant; they clarify prior uncertainties associated with the relationship between the NAO and the North Atlantic SSTA tripole.

Amidst stormy atmospheric circulation, there are prominent recurrent patterns of variability in the planetary circulation, such as the Antarctic Oscillation (AAO), Arctic Oscillation (AO) or North Atlantic Oscillation (NAO), and the Pacific–North America (PNA) pattern. The role of the synoptic eddy and low-frequency flow (SELF) feedback in the formation of these dominant low-frequency modes is investigated in this paper using the linear barotropic model with the SELF feedback proposed in Part I. It is found that the AO-like and AAO-like leading singular modes of the linear dynamical system emerge from the stormy background flow as the result of a positive SELF feedback. This SELF feedback also prefers a PNA-like singular vector as well among other modes under the climatological conditions of northern winters. A model with idealized conditions of basic mean flow and activity of synoptic eddy flow and a prototype model are also used to illustrate that there is a natural scale selection for the AAO- and AO-like modes through the positive SELF feedback. The zonal scale of the localized features in the Atlantic (southern Indian Ocean) for AO (AAO) is largely related to the zonal extent of the enhanced storm track activity in the region. The meridional dipole structures of AO- and AAO-like low-frequency modes are favored because of the scale-selective positive SELF feedback, which can be heuristically understood by the tilted-trough mechanism.